The music was written by Gabriel Ruiz (composer), the original Spanish lyrics by Ricardo López Méndez, with English lyrics written by Sunny Skylar. The original title and opening line "Amor, Amor, Amor" became "More and more Amor" in the English version. The song was published in 1943.
The recording by Bing Crosby was released by Decca Records as catalog number 18608. It first reached the Billboard magazine Best Seller chart on June 29, 1944, and lasted 7 weeks on the chart, peaking at #4.  The flip side was "Long Ago (and Far Away)," which also charted, making this a two-sided hit.
The recording by Andy Russell was released by Capitol Records as catalog number 156. It first reached the Billboard magazine Best Seller chart on May 25, 1944, and lasted 8 weeks on the chart, peaking at #5. 
In 1961, American soul singer Ben E. King covered the song and it appears on his album Spanish Harlem. It was released as a single, and peaked at #18 on the Billboard Hot 100 and #10 on the R&B chart.
Rod McKuen recorded a disco version in 1977.
Julio Iglesias has recorded the original Spanish version.